I might be misinterpreting your friend's question, but if your friend knows very little about the subject and is expressing surprise that something so seemingly simple turns out to be so complicated, then maybe you should concentrate on explaining the Hopf fibration to him or her. There is an interesting visualization in Thurston and Levy's book Three-Dimensional Geometry and Topology. I think that anyone who successfully goes through the exercise of visualizing the Hopf fibration will be disabused of any preconception that the homotopy groups "should" be simple.